Question

Produtos notáveis resolva :
a) (5-x)³
b) (1-3a²)³
c) (x/3 +2)³
d) ( 2x/3 - y/2)³

Answer 1

Resposta:

a) [x] = [5]

b) [a1] = [0,5773560145661699]

[a2] = [-0.5773473965013551]

[a3] = [0.5773473963399387]

[a4] = [0.5773560148890017]

c) [x] = [-6]

d) [y] = [52]

Answer 2

Reposta:

A) (5 - x)³ = 125 - 75x + 15x² - x³

B) (1 - 3a²)³ = 1 - 9a² + 27a^4 - 27a^6

C) (x/3 + 2)³ = x³/27 + (6x²/9) + (12x/3) + 8

D) (2x/3 - y/2)³ = (8x³/27) - (12x²y/18) + (6xy²/12) - (y³/8)

Explicação passo a passo:

CUBO DA SOMA/DIFERENÇA DE DOIS TERMOS, formula:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a – b)³ = a³ – 3a²b + 3ab² – b³

A) (5 - x)³

5³ - 3.5².x + 3.5.x² - x³

125 - 75x + 15x² - x³

B) (1 - 3a²)³

1³ - 3.1².3a² + 3.1.(3a²)² - (3a²)³

1 - 9a² + 27a^4 - 27a^6

C) (x/3 + 2)³

(x/3)³ + 3.(x/3)².2 + 3.(x/3).2² + 2³

x³/27 + (6x²/9) + (12x/3) + 8

D) (2x/3 - y/2)³

(2x/3)³ - 3.(2x/3)².(y/2) + 3.(2x/3).(y/2)² - (y/2)³

(8x³/27) - (12x²y/18) + (6xy²/12) - (y³/8)